How do I change my Objects' local axis?
There are several ways to do this:
1: use an armature, slow to make, but makes it much easier for animation.
2: set the 3D cursor to the parents origin, right click on the child, click on, set origin - to 3D cursor. ( this won't work if you want the robot to rotate the children indipendently later. (not recomended for animation)
3: to rotate them, select the parts you want to rotate, with the parent selected last.  set the pivot point to active element and rotate them. (also not reccomended for animation.)

There are other ways to do this too, but I hope this helped.

ps, I think the armature is the best  method, but If you just want to pose your robot for a still image, the other methods will help you.